Try the Federal Premium 85gr HPBT, I've killed about 35 deer with it, excellent bullet...

You don't have to give up on heavier bullets though...I've tested about 12 factory loadings in my .243...Some bullets just don't shoot well in some rifles...For some reason my rifle loves the 100gr Remington CoreLokts, the Federal Premium 85gr, the Federal Premium 100gr Nosler Partition and the Federal 100gr Hotcore...It doesn't like Hornadys, in the Lite Mag or standard loading, nor does it care for the Federal Premium 100gr Sierra GameKing SPBT or the Winchester Supremes 95gr Combined Technology...Some of these grouped up to 4 inches, whereas theCoreLokts will hit a quarter at 100 yards...

Keep trying until you find what your rifle prefers...